Figure 1.
Community and Community Core Detection Results.
From left to right, the three columns are corresponding to the years 1995, 2002, and 2011, respectively. The first row shows the Newman-Girvan community detection results. The America community is colored yellow, the Europe community is colored red, and the Asia-Oceania community is colored blue. Asia-Oceania and America were separated from each other in 1995 and 2011 but was integrated in 2002. The second row shows the community core detection results by normalizing for each community. The redness of each country is proportional to its relative magnitude of
within its community (CS). The reddest country in the Asia-Oceania community was Japan back in 1995 but became China in 2011. Finally, the third row provides a topological view of the community structure in the three years. Only the edges with no less than 10 million US dollars are shown. Again, Japan was central in the Asia-Oceania community in 1995 and it was replaced by China in 2011.
Figure 2.
The 95% confidence interval is calculated for each value of from 0.1 to 0.9 with the step size of 0.05 (the x-axis). The simulation is based on a dynamic-edge-weight mechanism for both inter- and intra-communities. Other model parameters are
,
, and
, respectively. We define a trial of simulation as running the dynamic-edge-weight mechanism for 5000 periods. As an indicator of the community structure stability of the network, the y-axis is the percentage of the number of the periods with exactly the same community structure as the initial status out of the 5000 periods. Finally, for each value of
, we estimate the confidence interval of the original community structure percentage by collecting a 100-trial sample.
Figure 3.
The figure is based on a single trial of simulation. Different colors represent different communities detected by the Newman-Girvan method. The inter-community edges are colored red while the intra-community ones are colored black. Although the community detection takes into account the edge weights, all the edges in the figure have the same width. In period 1, three predetermined communities, X1-X5, X6-X10, and X11-X15, are imposed in the network. The number of communities detected in this 15-node network bounces back and forth between 3 and 2 during the simulated periods. That is, like what we observe from the ITN, the disappearance and reemergence of the communities can be generated by the dynamic-edge-weight mechanism for both inter- and intra-communities.
Figure 4.
Inter- versus Intra-Community Trade Ratio between Asia-Oceania and America.
We calculate the ratio of the inter-community trade to the intra-community trade between the Asia-Oceania community and the America community. The ratio first went up and then went down and formed a hump shape over time. This finding coincides with the disappearance and reemergence of the Asia-Oceania community observed in Figure 1.
Figure 5.
Intra- and Inter-Community Strength of Japan and China.
We calculate both the inter- and intra-community trade volumes for Japan and China. Japan had more inter-community trade than China before 2003. However, after 2003, China surpassed Japan in terms of both inter- and intra-community trade. This finding coincides with the leadership change from Japan to China observed in Figure 1. Furthermore, for both countries, the intra-community trade follows closely to the inter-community trade, which can be viewed as evidence of the intra-community dynamic-edge-weight mechanism.
Table 1.
China's Effective RTAs.